A solution to a fractional order semilinear equation using variational method

IF 0.4 Q4 MATHEMATICS, APPLIED Mathematics in applied sciences and engineering Pub Date : 2020-11-09 DOI:10.5206/mase/9413
R. Karki
{"title":"A solution to a fractional order semilinear equation using variational method","authors":"R. Karki","doi":"10.5206/mase/9413","DOIUrl":null,"url":null,"abstract":"We will discuss how we obtain a solution to a semilinear pseudo-differential equation involving fractional power of laplacian by using a method analogous to the direct method of calculus of variations. More precisely, we will discuss the existence of a minimizer of a suitable energy type functional whose Euler-Lagrange equation is the given semilinear pseudo-differential equation, and also discuss the regularity of such a minimizer so that it will be a solution to the semilinear equation.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"1 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics in applied sciences and engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5206/mase/9413","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1

Abstract

We will discuss how we obtain a solution to a semilinear pseudo-differential equation involving fractional power of laplacian by using a method analogous to the direct method of calculus of variations. More precisely, we will discuss the existence of a minimizer of a suitable energy type functional whose Euler-Lagrange equation is the given semilinear pseudo-differential equation, and also discuss the regularity of such a minimizer so that it will be a solution to the semilinear equation.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
用变分法求解一类分数阶半线性方程
我们将讨论如何用一种类似于直接变分法的方法求得一个包含分数阶拉普拉斯函数的半线性伪微分方程的解。更确切地说,我们将讨论在给定的半线性伪微分方程为欧拉-拉格朗日方程的合适能量型泛函的极小值的存在性,并讨论该极小值的正则性,使其成为半线性方程的解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
1.40
自引率
0.00%
发文量
0
审稿时长
21 weeks
期刊最新文献
Solution of fractional modified Kawahara equation: a semi-analytic approach Recovery of an initial temperature of a one-dimensional body from finite time-observations Multiscale modeling approach to assess the impact of antibiotic treatment for COVID-19 on MRSA transmission and alternative immunotherapy treatment options The minimal invasion speed of two competing species in homogeneous environment Assessing the impact of host predation with Holling II response on the transmission of Chagas disease
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1